Cremona's table of elliptic curves

574 = 2 · 7 · 41

Field	Data	Notes
Atkin-Lehner	2+ 7+ 41+	Signs for the Atkin-Lehner involutions
Class	574b	Isogeny class
Conductor	574	Conductor
∏ cp	4	Product of Tamagawa factors cp
Δ	310100175392 = 25 · 78 · 412	Discriminant
Eigenvalues	2+  2 -2 7+ -6 -4 -2  2	Hecke eigenvalues for primes up to 20
Equation	[1,1,0,-2221,29181]	[a1,a2,a3,a4,a6]
Generators	[39:42:1]	Generators of the group modulo torsion
j	1212480836738137/310100175392	j-invariant
L	1.8100407779088	L(r)(E,1)/r!
Ω	0.90654496508994	Real period
R	1.9966365129272	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	4592k2 18368c2 5166bc2 14350s2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 574b2

a2	a3	a5	a7	a11	a13	a17	a19	a23	a29	a31	a37	a41	a43	a47	a53	a59	a61	a67	a71	a73	a79	a83	a89	a97
+	2	-2	+	-6	-4	-2	2	0	0	0	10	+	4	8	-4	-8	10	-14	-12	-6	0	4	-14	-10

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Quadratic twists for elliptic curve 574b2

-4	8	-3	5	-7	-11	13	41
4592k2	18368c2	5166bc2	14350s2	4018h2	69454ba2	97006u2	23534m2

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Data from Elliptic Curve Data by J. E. Cremona.
Design inspired by The Modular Forms Explorer by William Stein.

Part of Computational Number Theory
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